Geometry Review Worksheet
Chapter 7
Name:
Pentagons ABCDE and PQRST are similar. Use this information for #1-4.
1. <B
3.
________
CD
EA
=
RS
?
2. <S
________
4.
?
PQ
=
DE
AB
5
1
=
7
x
For #5-12, solve for x.
5.
3
4
=
8
x
6.
7.
x 2
9
=
12
x
8.
9.
3
4
=
7
x
10.
x 10
4
=
x
9
12.
10
3
=
x 2 9
11.
x
x 5
=
24
34
13. Given that 3x = 7y, find the ratio of
x
x 9
=
5
8
x
in simplest form.
y
14. Given that 9x = 5y, find the ratio of y : x in simplest form.
(over)
For #15-17, find the missing length. Show work.
15. AB = 6, BC = 4, AE = 3, find ED.
use for #15-17
16. AB = 9, BC = 6, ED = 4, find AE.
17. BC = 3, AC = 11, AE = 6, find ED.
For #18-29, find the value of x.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
For #30-32, find the unknown lengths. Show work.
FJ
30.
6
31.
10
32.
JG
FG
FI
IH
4
3
6
5
3
6
FH
8
33. Two similar polygons are shown.
a) The scale factor of pentagon LITBR
to pentagon QWNHA is __________.
b) If x = 9, then y = __________.
c) If m<R = 100, then m<A = __________.
(over)
For #34-37, Use the pictures above to write the reason the triangles are similar.
34. If m<B = 60, m<C = 40, m<E = 60, and m<F = 40, then ΔABC ~ ΔDEF.
35. If
AB
BC
AC
=
=
, then ΔABC ~ ΔPQR.
PR
PQ
QR
36. If
DE
EF
=
and <E
QR
PQ
<Q, then ΔDEF ~ ΔPQR.
37. If XY || QR , then ΔPXY ~ ΔPQR.
For #38-42, find the scale factor of each pair of similar triangles. ΔABC ~ ΔPQR.
Then find the values of x and y. Show work.
38. Scale factor = ________
x = ________
y = ________
39. Scale factor = ________
x = ________
y = ________
40. Scale factor = ________
x = ________
y = ________
41. Scale factor = ________
x = ________
y = ________
42. Scale factor = ________
x = ________
y = ________
In #43-48, ΔTUX ~ ΔTVW.
43. If m<T = 59 and m<TXU = 45, then m<V = ________.
44. If m<T = 52 and m<TUX = 68 then m<W = ________.
45. If TX = 12, XW = 16 and TU = 9,
find UV.
46. If TU = 9, UV = 6 and XW = 18,
find TX.
47. If TX = 8, XW = 4 and VW = 15,
find UX.
48. If TU = 8, UV = 10 and UX = 12,
find VW.
49. The ratio of the angle measures in a triangle is 4 : 9 : 11. What is the measure of the largest
angle?
50. The ratio of the angle measures in a quadrilateral is 2 : 5 : 6 : 7. What is the measure of the
smallest angle?